# Curves over Finite Fields

Plot an arbitrary curve under modular arithmetic (i.e. over $$\mathbb{F}_p$$).
Enter curve parameters and press 'Draw!'.

Note: Choose $$p$$ prime (like ...,43,47,53,59,61,67,71,73,79,83,89,97,101,109,...), otherwise $$\mathbb{F}_p$$ won't be a field!

##### Curve Parameters

Curve: $$p$$:

##### Tips
• Click/tap a point to view its coordinates.
• No ideas? Try one of these (by clicking on it):
• $$y^2+y = 3*x^3 +2*x^2 + x + 1 \mod 53$$
• $$x^2 = y^2 \mod 109$$ - a cross
• $$y^2 = x^3 + 2*x + 1 \mod 53$$ - an elliptic curve
• $$x^2 + y^2 \lt 20 \mod 109$$ - would be filled circle in $$\mathbb{R}$$
• $$x * y \lt 14 \mod 109$$
• $$y = 2^x \mod 47$$
• Only interested in Elliptic Curves? Switch to a specialized version.

© Sascha Grau, 2017, 2018